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If $a$ and $b$ are positive integers satisfying $\cot^{- 1} a + \cot^{- 1} b = \cot^{- 1} 7$ , then the number of ordered pairs of $(a, b)$ is

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Important Questions on Inverse Trigonometric Functions

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

Considering only the principal values of inverse functions, the set

A = \{x \geq 0 : \tan^{- 1} (2 x) + \tan^{- 1} (3 x) = \frac{π}{4}\}

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Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

The value of

S = \sum_{n = 1}^{\infty} \tan^{- 1} \frac{2 n}{n^{4} + n^{2} + 2}

is equal to

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Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

2 \tan^{- 1} \frac{1}{5} + \sec^{- 1} \frac{5 \sqrt{2}}{7} + 2 \tan^{- 1} \frac{1}{8} =

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

0 \leq A \leq \frac{π}{4}

, then

\tan^{- 1} (\frac{1}{2} \tan 2 A) + \tan^{- 1} (\cot A) + \tan^{- 1} (\cot^{3} A)

is equal to

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

The value of

4 \tan^{- 1} (\frac{1}{5}) - \frac{π}{4} =

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

\cos^{- 1} (\frac{x}{2}) + \cos^{- 1} (\frac{y}{3}) = θ,

then

9 x^{2} - 12 x y \cos θ + 4 y^{2} =

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

\sum_{m = 1}^{n} \tan^{- 1} (\frac{2 m}{m^{4} + m^{2} + 2})

is equal to

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

\cot^{- 1} \frac{1}{5} + \cot^{- 1} \frac{1}{3} - \cot^{- 1} \frac{4}{7} = \cot^{- 1} x

, then

x

is equal to

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

α = {c o s}^{- 1} (\frac{3}{5})

β = {t a n}^{- 1} (\frac{1}{3})

, where

0 < α, β < \frac{π}{2},

then

α - β

is equal to

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

The value of

\sin^{- 1} (\frac{12}{13}) - \sin^{- 1} (\frac{3}{5})

is equal to:

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Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

\sin^{- 1} \frac{8}{17} + \sin^{- 1} \frac{3}{5}

is equal to

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

f (x) = 2 \tan^{- 1} x + \sin^{- 1} (\frac{2 x}{1 + x^{2}}), x > 1

, then

f (5)

is equal to

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

The value of

\sin (2 \sin^{- 1} 0.8)

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Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

\sum_{k = 1}^{n} \tan^{- 1} (\frac{1}{k^{2} + k + 1}) = \tan^{- 1} (θ)

, then

θ =

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Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

The value of the expression

\tan [(1 / 2) \cos^{- 1} (2 / \sqrt{5})]

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

\tan (\cos^{- 1} (\frac{1}{5 \sqrt{2}}) - \sin^{- 1} (\frac{4}{\sqrt{17}}))

MEDIUM

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

$\tan^{- 1} (\frac{x}{y}) - \tan^{- 1} \frac{x - y}{x + y}$ is equal to.

HARD

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

2 π - (\sin^{- 1} \frac{4}{5} + \sin^{- 1} \frac{5}{13} + \sin^{- 1} \frac{16}{65})

is equal to :

EASY

Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

\sin^{- 1} (\frac{x}{5}) + {c o s e c}^{- 1} (\frac{5}{4}) = \frac{π}{2},

then the value of

x

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Mathematics>Trigonometry>Inverse Trigonometric Functions>Identities of Inverse Trigonometric Functions

Let

\tan^{- 1} y = \tan^{- 1} x + \tan^{- 1} (\frac{2 x}{1 - x^{2}})

, where

|x| < \frac{1}{\sqrt{3}}

,Then a value of

y

If a and b are positive integers satisfying cot-1a+cot-1b=cot-17, then the number of ordered pairs of a, b is

Important Questions on Inverse Trigonometric Functions

Learn and Prepare for any exam you want !

If $a$ and $b$ are positive integers satisfying $\cot^{- 1} a + \cot^{- 1} b = \cot^{- 1} 7$ , then the number of ordered pairs of $(a, b)$ is